A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct^2 (a, b > 0). What is the meaning of the constant c?
(a) Uniform acceleration
(b) Non – uniform acceleration
(c) Uniform retardation
(d) Non – uniform retardation
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The question is from Calculus Application in section Application of Calculus of Mathematics – Class 12
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Correct answer is (a) Uniform acceleration
For explanation: We have, x = a + bt + ct^2 ……….(1)
Let, v and f be the velocity and acceleration of a particle at time t seconds.
Then, v = dx/dt = d(a + bt + ct^2)/dt = b + ct ……….(2)
And f = dv/dt = d(b + ct)/dt = c ……….(3)
Since f = dv/dt = c, hence, c represents the uniform acceleration of the particle.